The present invention relates to a signal generator which generates a test, signal for input to a device under test the output signal of which is analyzed by a fast Fourier transform analyzer, i.e. what is called a digital spectrum analyzer.
A fast Fourier transform analyzer (hereinafter referred to as the FFT analyzer) analyzes the response characteristic (the transfer function) of an electrical device, such as a transmission line, an amplifier, a filter or the like, when supplied with a test signal, or the response characteristic of a mechanical device, such as mechanical vibration or the like, when supplied with a mechanical test signal. In such an analysis, according to the prior art, a single spectrum, that is, a pure sine-wave signal is applied to the device under test and the frequency of the sine-wave signal is successively changed for the FFT analysis of the output signal from the device under test for each frequency. Accordingly, the conventional method, in which the test signal is produced for each frequency within a desired frequency range and the FFT analysis is conducted for each test signal, possesses the defect of extended measurement time.
On the other hand, it has been proposed to employ a noise generator as the signal generator as disclosed, for example, in U.S. Pat. No. 3,988,667 entitled "Noise Source for Transfer Function Testing", issued Oct. 26, 1976, or U.S. Pat. No. 4,023,098 entitled "Noise Burst Source for Transfer Function Testing", issued May 10, 1977. Since various spectra are provided from the noise generator simultaneously, the measurement time can be reduced. The FFT analyzer, however, is not able to analyze continuous frequency spectra and can analyze only discrete frequency spectra, so that unnecessary frequency components are applied to the FFT analyzer, causing a measurement error. This will hereinunder be described in brief.
In general, the FFT analyzer performs a discrete digital Fourier transformation of a signal by sampling it at 2.sup.n finite discrete sample points with a sampling period t.sub.0 in a finite time series, thereby analyzing 2.sup.n-1 spectra spaced 1/2.sup.n t.sub.0 (Hz) from one another. That is, signals at 2.sup.n discrete sample points in the time domain are mapped to a 2.sup.n -dimensional orthogonal Fourier space in the frequency domain. The Fourier space in which the signals are mapped is a complex plane representing 2.sup.n-1 spectra which are spaced 1/2.sup.n t.sub.0 (Hz) apart. Expressed in the time domain, the spectra are each given by the following expression: ##EQU1## When m is an integral value in the range from 0 to 2.sup.n-1 in the above expression (1), the signal can be correctly mapped to the Fourier transform mapping space by virtue of the orthogonality of the function. But when m is a non-integral value, for instance, 1.3, the spectrum component of the signal is not correctly mapped to the Fourier transform mapping space, but instead it is mapped to a plurality of complex spectral planes. This is commonly referred to as energy leakage in a finite time series. Accordingly, in the case of using a thermal noise generator or an M-series pseudo-random signal generator as the signal generator, the analysis result contains many frequency components resulting from the non-integral values of m in the above expression (1), and hence it has an error. To alleviate the energy leakage, it is customary in the prior art to multiply the time series data by a weighted function, for instance, W (t)=1+cos (2.pi./2.sup.n t.sub.0)t, and to subject the time series data to discrete Fourier transformation. But since this weighted function also acts on the information of as many sample points as 2.sup.n, the amount of information of the sample points themselves is partly lost, that is, leakage is caused in the vicinity of the correct spectrum to lower the spectral resolution, resulting in decreased measurement accuracy and narrowed dynamic range.
To raise the measurement accuracy, it is general practice in the prior art to conduct the measurement a plurality of times and to average the measured results. This method is, however, defective in that the measurement time is extended by such repeated measurement; in particular, when the measurement frequency is low, the sampling period is increased, resulting in the overall measurement time becoming appreciably long.
Furthermore, when analyzing a transfer function of a nonlinear device, it is desired to apply thereto a random signal having a suitable amplitude probability density distribution such as a Gaussian distribution or Poisson's distribution, for example. In such a case it has been the practice to provide a plurality of dedicated random signal generators respectively having desired amplitude probability density distributions, thus requiring an increased size and cost, as a whole.